Quick questions on Electromagnetic induction: HSC Physics Module 6

For a single conducting loop linked by a magnetic flux $\Phi(t)$, the induced EMF around the loop is:

The induced EMF and induced current always act in a direction that opposes the change in flux that produced them.

A conducting rod of length $L$ moving with velocity $v$ perpendicular to a uniform field $B$ (and with $L$, $v$ and $B$ mutually perpendicular) has free charges in it experiencing a magnetic force $F = qvB$ along the rod. Charge separates until an electric field inside the rod balances the magnetic force. The resulting EMF between the ends of the rod is:

When a bulk conductor (a sheet, disc or block of metal) experiences a changing flux, induced EMFs drive circulating currents called eddy currents inside the conductor. They oppose the change in flux that produced them, so they exert a drag force on whatever is causing the flux change.

An induction coil is a transformer-like device used to produce high-voltage pulses from a low-voltage DC source. It has:

A 100-turn rectangular coil of area $0.020$ m$^2$ rotates at $50$ Hz in a uniform field of $0.10$ T. Find the peak induced EMF.

A 100-turn coil with a flux change of 1 Wb produces 100 times more EMF than a single loop with the same change.

The minus sign encodes Lenz's law. Most numerical problems ask for the magnitude; a separate sentence then explains direction using Lenz's law.

A large steady flux produces no EMF. Only a changing flux does.

It is Faraday's law applied to a bulk conductor, plus resistive dissipation of the induced currents.